doi:10.14492/hokmj/2020-422engArtal Bartolo, E.Morón-Sanz, R.Differential geometry of complex projective plane conicsART-2023-136448In this paper we study properties of complex plane projective curves from a geometric point of view. We focus our attention on properties of conics. We find that Gauss curvature determines a conic up to a hermitian transformation preserving the Fubini-Study metric of the complex projective plane and we discuss some other geometric properties of the conics. Finally we study the deformation of smooth conics onto pair of lines and the classification of cubics up to hermitian transformations.2023http://zaguan.unizar.es/record/13014210.14492/hokmj/2020-422http://zaguan.unizar.es/record/130142oai:zaguan.unizar.es:130142info:eu-repo/grantAgreement/ES/DGA/E22-20Rinfo:eu-repo/grantAgreement/ES/MICINN/MTM2016-76868-C2-2-Pinfo:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033info:eu-repo/grantAgreement/ES/MICINN/PID2020-118425GB-I00HOKKAIDO MATHEMATICAL JOURNAL 52, 1 (2023), 23-40All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess